When I start loading the video, the memory usage under /tmp goes up and up until it reaches 100%, then the video stops downloading. After searching for a while, I learned that tmpfs will use RAM first (if I got it correctly, the 302MB in /tmp), then going for swap space. But it seems not to be using my swap space.Swap space seems to be correctly mounted and activated:

First of all, are my assumptions above correct? That is: fstab is properly indicating my swap drives, swap is correctly mounted and activated and tmps should be but isn't using swap. Then, why am I not able to use more virtual memory for downloading the video?I read suggestions on moving Firefox cache to a directory in the hard drive, but this would make it quite slower for not so huge files. I also read directions to increase the /tmp RAM file, but I'm afraid this would make other stuff suffer on lack of RAM (plus it involves creating scripts I'm not comfortable with yet).What can I do?

AFAIK if tmpfs is set to 302 MiB size then it would never use more than that. The tmpfs filesystem shrinks and grows as needed, but you have set it to a limit of 302 MiB so it will never grow beyond that. It will swap out pages when not enough RAM is available to have 302 MiB, but never more than the 302 MiB size limit you have configured. If you want /tmp to be bigger than 302 MiB, make it so.

Looking at your fstab, I can't see how you have configured /tmp to be tmpfs? Perhaps this is something done automatically by LMDE? You should be able to add an entry to fstab to override any LMDE defaults. For example as such to give it a 500 MiB size limit:

Edit: looking at the blkid output it is ext4. So delete the second entry for /dev/sda1 (the ext3 one), and replace the final 0 (zero) on the first entry for /dev/sda1 (the ext4 one) to 1 (one) to indicate you want fsck to check this filesystem on boot.

Yes, this is all automatically done by LMDE. I'm not much experienced in Linux, so I don't mess too much on things unless I have a problem.So the problem is that tmpfs was limited by the system defaults. So it would never grow enough to use swap, even when required to grow more.I learned that I can set limits for /tmp (and other directories mounted as tmpfs, like /run, /run/lock or /run/shm) in fstab, but this is an option. There's another way to set those limits, and also the global tmpfs limit. They are spec'ed in /etc/default/tmpfs (deprecated, so I'll probably use fstab in the future):

The "TMPFS_SIZE" variable sets the global limit, and was set to 20%. Since I have 1.5GiB of RAM, then my global tmpfs size was 302MiB, less than the video size.I ran top with lots of apps opened (including VirtualBox and Firefox with several tabs open) and saw I still had almost 200MiB of free RAM. So I changed the global tmpfs limit to 30% as shown above. Rebooted (since I don't know how to restart tmpfs) and watched the video without problems.

As for the weird inputs in fstab: man, I had double inputs for both /dev/sda1 and /proc! Commented out the wrong /dev/sda1 line and corrected the fsck argument as you said. Do you have a hint on how to tell which of the /proc lines is correct? Only the mount options are different: